Snapping Vertices to One Vertex on a UV Map
Try using G instead.
By clicking with  RMB, you are deselecting everything but the vertex under the cursor, which will then be translated.

Translating/grabbing with the mouse is sort of intended as a convenience thing to quickly be able to tweak individual vertices without pressing G.

The reason why it can't work for translating a selection of multiple elements is because  RMB is already used primarily for selecting. So clicking will first select the vertex under the cursor, then after moving the cursor 10px with the mouse button held, the grab/translate operator is called. This 10px threshold is configurable in &#9096; Ctrl&#9095; AltU> User preferences > Input > Tweak Threshold:



In most places and most of the time you'll want to use G for translating/grabbing.